Similarity and Congruence
Understand similarity, congruence, and scale factors in MYP Maths Year 5. SSS, SAS, ASA criteria, area and volume scaling, and exam question strategies covered.
What This Topic Covers
Similarity and congruence form a cornerstone of geometric reasoning in MYP Year 5. Students distinguish between shapes that are the same size and orientation (congruent) and shapes that are proportionally scaled versions of each other (similar), then use these properties to solve problems involving unknown lengths and angles.
Congruence Criteria
Two triangles are congruent if they satisfy one of the following conditions:
- SSS — three sides equal
- SAS — two sides and the included angle equal
- ASA — two angles and the included side equal
- AAS — two angles and a non-included side equal
- RHS — right angle, hypotenuse, and one other side equal
Students must be able to state which criterion applies and justify why two triangles are congruent in formal geometric language.
Similarity and Scale Factors
Similar shapes have equal corresponding angles and proportional corresponding sides. The scale factor k links corresponding lengths. Area scales by k² and volume by k³ — a common source of exam errors when students apply the linear scale factor to area or volume directly.
Finding Missing Lengths
Set up a proportion using corresponding sides. Identify the scale factor first, then multiply or divide as required. Always confirm which sides are truly corresponding before writing the ratio.
Common Mistakes
- Applying the linear scale factor to area (should be k²)
- Matching non-corresponding sides in a proportion
- Stating SSA as a valid congruence criterion — it is not
- Confusing similarity with congruence in written justifications
MYP Question Style
Questions may present two triangles with some sides or angles labelled and ask students to prove congruence or similarity, then use the result to find a missing length. Criterion A tasks often embed similarity within a diagram of overlapping triangles where corresponding vertices must be identified carefully.
Practice Approach
Practise identifying similar triangles inside larger geometric figures — parallel lines cutting transversals often produce embedded similar triangles. Work on area and volume scale-factor problems separately until the k, k², k³ relationship feels automatic.